Théorème d'Erdős-Kac dans presque tous les petits intervalles

Abstract

We show that the Erdős-Kac theorem is valid in almost all intervals $\left[x,x+h\right]$ as soon as $h$ tends to infinity with $x$. We also show that for all $k$ near $\log \log x$, almost all interval $\left[x,x+\exp \left({\left(\log \log x\right)}^{1/2+\epsilon }\right)\right]$ contains the expected number of integers $n$ such that $\omega (n)=k$. These results are a consequence of the methods introduced by Matomäki and Radziwiłł to estimate sums of multiplicative functions over short intervals.

16 pages, in French. Corrected typos, added e-mail address

References in corpus (2)

• An averaged form of Chowla's conjecture
• Almost Primes in Almost All Short Intervals

Cited by in corpus (1)

• On the Twin Prime Conjecture